Formulas on Physics - Assignment Example

1-24-A 4-m pole is supported at each end by hunters carrying an 800-N deer which is hung at a point 5 m from the left end. What is the upward forcerequired by the hunter on the left end? 800 N (2.5 m) - F (4 m) = 0 --- F = 500 N 25-A person who weighs 650 N rides a bicycle. The pedals move in a circle of radius 40 cm. If the entire weight acts on each downward moving pedal, what is the maximum torque? T = 650 N (0.4 m) = 260 N*m 26-Compute the center of gravity of sledgehammer if the metal head weighs 12 lb and the 32-in. supporting handle weighs 2 lb. Assume that the handle is of uniform construction and weight.  Give your answer in terms of inches of distance from the head of the sledgehammer. 12 lb (x) - 2 lb (32/2 in.) = 0 --- x = 2.67 in. 27-A uniform 6-m bar has a length of 6 m and weighs 30 N. A 50-N weight is hung from the left end and a 20-N force is hung at the right end. How far from the left end will a single upward force produce equilibrium? Fx - 30 N (3 m) - 20 N (6 m) = 0 ; 30 N (3m) + 50 N (6 m) - F (6 – x) = 0 --- Combining: 90 + 300 - 6F + 210 --- F = 100 N 28-A leather belt is wrapped around a pulley 20 cm in diameter. A force of 60 N is applied to the belt. What is the torque at the center of the shaft? T = 60 N (0.10 m) = 6 N*m 29-A 40-N sphere and a 12-N sphere are connected by a light rod 200 mm in length. How far from the middle of the 40-N sphere is the center of gravity? Give your answer in millimeters. 40 N (x) - 12 N (200 - x) = 0 --- x = 46.15 mm 30-What is the magnitude of the moment arm around point A? Give your answer in feet. 31-A 10-ft platform weighing 40 lb is supported at each end by stepladders. A 180-lb painter is located 4 ft from the right end. Find the force exerted by the left support.  Give your answer in pounds. -R (10 ft) + 40 lb (5 ft) + 180 lb (4 ft) = 0 --- R = 92 lb 32-An 8-m board of negligible weight is supported at a point 2 m from the right end where a 50-N weight is attached. What downward force at the must be exerted at the left end to produce equilibrium? -F (8 m) + 50 N (2 m) = 0 --- F = 12.5 N 33-Weights of 2, 5, 8, and 10 N are hung from a 10-m light rod at distances of 2, 4, 6, and 8 m from the left end. How far from the left in is the center of gravity? 2 N (2 m) + 5 N (4 m) + 8 N (6 m) + 10 N (8 m) = x (25 N) --- x = 6.08 m 34-A baseball leaves the bat with a velocity of 30 m/s at an angle of 300. What is the horizontal component of its velocity after 3 s? Vx = (30 m/s) (cos 30°) = 25.98 m/s 35-A projectile has an initial horizontal velocity of 40 m/s at the edge of a roof top. Find the horizontal component of its velocity after 3 s. Vx = 40 m/s 36-A ball is dropped from rest and falls for 5 s. What is its position? position, x = 0 + g = (9.81) (5)2 --- x = 122.6 m 37- The tip of a robot arm is moving to the right at 8 m/s. Four seconds later, it is moving to the left at 2 m/s. What is the acceleration. a = = --- a = 1.5 m/s2 38-A small rocket leaves its pad and travels a distance of 40 m vertically upward before returning to the earth five seconds after it was launched. What was the average velocity for the trip? ave. velocity = = 8 m/s 39-A bullet leaves a 28-in. rifle barrel at 2700 ft/s. What was its time in the barrel in milliseconds? t = * * = 0.864 ms 40-A truck traveling at 60 mi/h brakes to a stop in 180 ft. What was the average acceleration?  Give your answer in feet per second squared. 60 mi/h  88 ft/s (upon conversion) 0 = (88 ft/s)2 - 2a (180 ft) --- a = 21.51 ft/s2 41-An arresting device on a carrier deck stops an airplane in 1.5 s. The average acceleration was 49 m/s2. What was the stopping distance? V0 = (49 m/s2) (1.5 s) = 73.5 m/s and 0 = V02 - 2ad --- d = = = 55.13 m 42- Copy of A bullet leaves a 28-in. rifle barrel at 2700 ft/s. What was its time in the barrel in milliseconds? t = * * = 0.864 ms 43-A monorail train traveling at 22 m/s must be stopped in a distance of 120 m. What is the stopping time? 0 = (22 m/s)2 - 2a (120) --- a = 2.0167 m/s2 0 = V0 - at --- 0 = 22 m/s - (2.0167 m/s2)*t --- t = 10.9 secs 44-Three masses, 2 kg, 4 kg, and 6 kg, are connected (in order) by strings and hung from the ceiling with another string so that the largest mass is in the lowest position.  If the system feels only an acceleration upward at 4 m/s2, what is the tension in the cord that separates Block B and Block C? FBD about C: TBC - 6 kg (9.81 m/s2) = 6 kg (4 m/s2) --- TBC = 82.86 N 45-Three masses, 2 kg, 4 kg, and 6 kg, are connected (in order) by strings and hung from the ceiling with another string so that the largest mass is in the lowest position. What is the tension in the cord that separates Block A and Block B? T(top) - 6 kg (9.81 m/s2) = (2 kg + 4 kg + 6 kg) ( 4 m/s2) T(top) = 106.86 N ; T(top) - TAB - 2 kg (9.81 m/s2) = 2 kg (4 m/s2) --- TAB = 79.24 N 46-Find the mass of a body if a resultant force of 400 N causes it to decrease its velocity by 4 m/s in 3 s. a = = 1.333 m/s2 and F = ma --- 400 N = m (1.333 m/s2) --- m = 300 kg 47-A 20-kg mass hangs at the end of a rope. Find the acceleration of the load if the tension in the cable is 260 N. F = ma --- 260 N = (20 kg) (a) --- a = 13 m/s2 48-Find the weight of a body if a resultant force of 400 N causes it to decrease its velocity by 4 m/s in 3 s. A = = 1.333 m/s2 --- 400 N = m (1.333 m/s2) --- m = 300 kg and W = mg = (300 kg) (9.81 m/s2) = 2943 N 49-Two masses (m1=2kg and m2=8kg), connected by a cord, hang straight down from either side of a light frictionless pulley. What is the acceleration of the system? 2(9.81 m/s2) - 8(9.81 m/s2) = (a) (2 + 8) kg --- a = -5.9 m/s2 50- An 800-kg elevator is lifted vertically by a strong rope. Find the acceleration of the elevator if the rope tension is 7840 N. 7840 N - 800 kg (9.81 m/s2) = (800 kg) (a) --- a = -0.01 m/s2 51-What is the mass of a 40-N tank? W = mg --- 40 N = m*(9.81 m/s2) --- m = 4.08 kg 52-Three masses, 2 kg, 4 kg, and 6 kg, are connected (in order) by strings and hung from the ceiling with another string so that the largest mass is in the lowest position.  If the system feels only an acceleration upward at 4 m/s2, what is the tension in the cord that separates Block A and Block B? T(top) - 6 kg (9.81 m/s2) = (2 kg + 4 kg + 6 kg) ( 4 m/s2) T(top) = 106.86 N ; T(top) - TAB - 2 kg (9.81 m/s2) = 2 kg (4 m/s2) --- TAB = 79.24 N 53-Find the weight of a body if a resultant force of 16 N will give it an acceleration of 5 m/s2. F = ma --- 16 N = m*(5 m/s2) --- m = 3.2 kg W = mg = (3.2 kg) (9.81 m/s2) = 31.4 N 54-A 500-g block is released from the top of a 30° inline and slides 160 cm to the bottom. A constant friction force of 0.9 N acts the entire distance. What work is done by friction? W = F*d = 0.9 N (1.60 m) = 1.44 N*m 55-A 5-kg hammer is lifted to a height of 3 m. What is the minimum required work? minimum W = (5 kg) (9.81 m/s2) (3 m) = 147.15 N*m 56-A trunk is dragged a horizontal distance of 24 m by a rope that makes an angle θ with the floor. If the rope tension is 80 N, what work is done for an angle of 60°? W = F*d cos θ = (80 N) (24 m) (cos 60°) = 960 N*m 57-A 10-kg block is dragged 20 m by a parallel force of 26 N. If μk = 0.2, what acceleration results? friction force = 0.2 (10 kg) (9.81 m/s2) = 19.62 N (10)(a) = 26 N - 19.62 N --- 0.638 m/s2 58- A 300-kg elevator is lifted vertical distance of 100 m in 2 min. What is the output power? output power = = = 2452.5 watts 59- A 40-kg mass is lifted through a distance of 20 m in a time of 3 s. Find average power. ave. power = = = 2616 watts 60- A 1.2 kg brick is held a distance of 2 m above a manhole and then dropped. The bottom of the manhole is 3 m below the street. Relative to the street, what is the potential energy of the brick at the bottom of the manhole? potential energy, PE = mgh = (1.2 kg) (9.81 m/s2) (5 m) = 58.86 J Read More