At hokey puck of mass 0.17 kg is shot across a rough floor with the roughness different at different places, which can be described by a position-dependent coefficient of kinetic friction. For a puck moving along the x-axis, the coefficient of kinetic friction is the following function of x, where x is in m: µ (x) = 0.1 + 0.05x. Find the work done by the kinetic frictional forte on the hockey puck when it h moved (a) from x = 0 to x = 2 m
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- (a) A block with a mass m is pulled along a horizontal surface for a distance x by a constant force F at an angle e with respect to the horizontal. The coefficient of kinetic friction between block and table is u. Is the force exerted by friction equal to u, mg? If not, what is the force exerted by friction? (Assume 0 is measured above the horizontal.) This answer has not been graded yet. (b) How much work is done by the friction force and by F? (Don't forget the signs. Use the following as necessary: F for the magnitude of F, g, m, x, 0 and u,) WE = (c) Identify all the forces that do no work on the block. (Select all that apply.) O friction f OF Cos(e) OF sin(0) O mE (d) Let m = 2.00 kg, x = 4.50 m, 0 = 3.7°, F = 14.5 N, and u, = 0.400, and find the answers to parts (a) and (b). (Include appropriate signs.) We = W =a 2.5 kg mass is intially at reston a horizontal surface. an applied force acts in the +x direction resulting in a displacement of 1.50 m. if the speed of the mass is 4.00 m at the 150 m mark and the applied force is 22.0 N what amount of work was done by friction?On an essentially frictionless, horizontal ice rink, a skater moving at v = 3.0 m/s encounters a rough patch that reduces her speed to 45% due to a friction force that is 25% of her weight (w). Use the work-energy theorem to find the length of this rough path.Express first your answer in terms of any or all of the variables v, w, and g (acceleration due togravity), and then its numerical value
- Air bags are used in cars to decelerate the occupants slowly when a car is suddenly decelerated in a crash. (a) Compute the work done by the decelerating force acting on a 55.0 kg driver if the car is brought to rest from an initial speed of 20.0 m/s. (b) Find the minimum thickness of the air bag if the average decelerating force is not to exceed 8900 N (2000 lb), and the center of the car moves forward 0.800 m during impactA block of mass m=1.5kg is released from rest at an unknown height h. The coefficient of friction between the block and the incline oriented at an angle of 0=56° is Hk=0.21. If the speed of the block v=4.1m/s when it leaves the inclined plane, determine the work done by the force of gravity. Take g =9.81m/s? and express your final result using one decimal place. m mThe force required to compress a non-standard spring as a function of displacement is given by the equationF(x) = -Asin(bx) + kx,where A = 25 N, b = 11 rad/m, and k = 68 N/m. Enter a general equation in terms of the given variables for the work required to compress this spring from position x1 to x2. Calculate the work done in joules as the spring is compressed from x = 0 to x1 = 21 cm. Calculate the work done in joules as the spring is compressed from x1 = 21 cm to x2 = 66 cm
- Starting from rest, a 5.00-kg block slides 2.50 m down a rough 30.0incline. The coefficient of kinetic frictionbetween the block and the incline is μk=0.436. Determine (a) the work done by the force of gravity, (b) the work done by the friction force between block and incline, and (c) the work done by the normal force. (d) Qualitatively, howwould the answers change if a shorter ramp at a steeper angle were used to span the same vertical height?A 17.9 kg block is dragged over a rough, horizontal surface by a constant force of 111 Nacting at an angle of angle 31.1◦above the horizontal. The block is displaced 60 m and the coefficient of kinetic friction is 0.152. Find the work done by the 111 N force. The acceleration of gravity is 9.8 m/s2.Answer in units of J. Find the magnitude of the work done by the force of friction.Answer in units of J What is the sign of the work done by the frictional force?1. positive2. negative3. zero Find the work done by the normal force.Answer in units of J What is the net work done on the block?Answer in units of J.A block of mass m is on an inclined ramp. The ramp makes anangle θ with respect to the horizontal, as shown. The ramp hasfriction, with coefficient of kinetic friction μk and static friction μs.This experiment takes place on earth.The block has an initial speed of v up the ramp. It travels adistance d along the ramp before it stops.Answer using variables, please d) Calculate the work done by the Friction force as the block travels the distance d.Is it positive, negative, or zero?e) If the block comes to rest, how far has it travelled?Use the work-energy principle and your results of parts b), c), and d).f) Briefly (one sentence) explain why this problem could not be solved using conservation ofenergy.
- Suppose the ski patrol lowers a rescue sled and victim, having a total mass of 85.0 kg down a 60° slope at constant speed, as shown in the figure. The coefficient of friction between the sled and the snow is 0.100. (a) How much work is done by friction as the sled moves 30.0 m along the hill. Enter to 3 significant figures W fric (b) How much work is done by the rope on the sled in this distance? Hint: use Newton's second law to find the tension. Enter to 3 significant figures Wrope W. grav 60° J (c) What is the work done by the gravitational force on the sled? Enter to 3 significant figures J W₁ W J (d) What is the work done by the normal force? WN= J total (e) What is the total work done? Enter to 3 significant figures Note: When adding work done by individual forces, DO NOT ROUND THE VALUES TO FIND THE SUM. J Sense-making: If the speed of the rescue sled & the victim is constant, what do you expect the total work done on the rescue sled and the victim to be? Does your answer support…A 7.80 g bullet is moving at 460 m/s just before it penetrates a tree trunk to a depth of 4.9 cm (ay What the magnitude of the average frletional force (In N) that is exerted on the bullet whille moving the tree trunk? Uso work considerations to o your answer. (b) Asturing the frictional force is constant, how much time elapses between the moment the bullet enters the tree trunk and the moment it moving?A 35 kg sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 10.0 m/s, and its velocity at point B is 2.0 m/s. You must use Work/Energy methods (not Kinematics). (a) What is the frictional force acting on the sled? (b) How much work is done on the sled by friction over the displacement ∆x = xB − xA? (c) What is the distance the sled travels between A and B?