A mass m = 12 kg rests on a frictionless table and accelerated by a spring...

A mass m = 12 kg rests on a frictionless table and accelerated by a spring with spring constant k = 5249 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is μ_k = 0.49. The mass leaves the spring at a speed v = 3.2 m/s.

A)How much work is done by the spring as it accelerates the mass?
B)How far was the spring stretched from its unstreched length?
C)

The mass is measured to leave the rough spot with a final speed v_f = 1.9 m/s.

How much work is done by friction as the mass crosses the rough spot?
D)What is the length of the rough spot?
E)In a new scenario, the block only makes it (exactly) half-way through the rough spot. How far was the spring compressed from its unstretched length?
F)In this new scenario, what would the coefficient of friction of the rough patch need to be changed to in order for the block to just barely make it through the rough patch?

Expert Solution

genius_generous answered 1 hour ago

A mass m = 17 kg rests on a frictionless table and accelerated by a spring...

A mass m = 17 kg rests on a frictionless table and accelerated by a spring with spring constant k = 4916 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is μk = 0.47. The mass leaves the spring at a speed v = 3.2 m/s. 1) How much work is done by the spring as it accelerates the mass? 2) How far was the spring stretched from its unstreched...

A mass m = 16 kg rests on a frictionless table and accelerated by a spring...

A mass m = 16 kg rests on a frictionless table and accelerated by a spring with spring constant k = 4739 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is μk = 0.45. The mass leaves the spring at a speed v = 2.9 m/s. 1)How much work is done by the spring as it accelerates the mass? 2)How far was the spring stretched from its unstreched length? 3)The...

A block with a mass of m = 33 kg rests on a frictionless surface and...

A block with a mass of m = 33 kg rests on a frictionless surface and is subject to two forces acting on it. The first force is directed in the negative x-direction with a magnitude of F1 = 11.5 N. The second has a magnitude of F2 = 23 N and acts on the body at an angle θ = 22° measured from horizontal, as shown. write an expression for the component of net force, Fnet,x, in the x...

A mass m1 = 5.6 kg rests on a frictionless table and connected by a massless...

A mass m1 = 5.6 kg rests on a frictionless table and connected by a massless string to another mass m2 = 5.7 kg. A force of magnitude F = 44 N pulls m1 to the left a distance d = 0.88 m. Initally both blocks are at rest. 1) How much work is done by the force F on the two block system? J 2) How much work is done by the normal force on m1 and m2? J...

A mass m1 = 4.4 kg rests on a frictionless table and connected by a massless...

A mass m1 = 4.4 kg rests on a frictionless table and connected by a massless string over a massless pulley to another mass m2 = 3.8 kg which hangs freely from the string. When released, the hanging mass falls a distance d = 0.7 m. 1)How much work is done by gravity on the two block system? 2)How much work is done by the normal force on m1? 3)What is the final speed of the two blocks? 4)How much...

A mass m1 = 4.7 kg rests on a frictionless table and connected by a massless...

A mass m1 = 4.7 kg rests on a frictionless table and connected by a massless string over a massless pulley to another mass m2 = 4.3 kg which hangs freely from the string. When released, the hanging mass falls a distance d = 0.76 m. 1. How much work is done by gravity on the two block system? 2. How much work is done by the normal force on m1? 3. What is the final speed of the two...

A block rests on a horizontal frictionless table. It is attached to a spring and set...

A block rests on a horizontal frictionless table. It is attached to a spring and set into motion. Consider what will happen to the frequency or period in each of the following situations. (increase, decrease, or stay the same) If the spring constant is cut in half (looser spring), the frequency will _______. If the spring constant is cut in half (looser spring), the period will _______. If the amplitude of the motion is doubled, the frequency will ______. If...

A block with mass M1 rests on a frictionless table. It is connected by a massless...

A block with mass M1 rests on a frictionless table. It is connected by a massless string to a block with mass M2, which hangs below the edge of the table. The system is released from rest at time t = 0. Find the distance block M1 moves in time t. You may assume that the string passes over a massless, frictionless pulley at the edge of the table to assist your calculations.

1) A ladder whose length L is 12 m and mass m are 45 kg rests...

1) A ladder whose length L is 12 m and mass m are 45 kg rests against a wall. Its upper end is a distance h of 9.3 m above the ground. The center of mass of the ladder is one-third of the way up the ladder. A fire fighter whose mass M is 72 kg climbs the ladder until his center of mass is halfway up. Assume the wall but not the ground is frictionless. What forces are exerted...

A textbook of mass 2.06 kg rests on a frictionless, horizontal surface. A cord attached to...

A textbook of mass 2.06 kg rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.100 m , to a hanging book with mass 2.99 kg . The system is released from rest, and the books are observed to move a distance 1.24 m over a time interval of 0.750 s. a) What is the tension in the part of the cord attached to the textbook? b) What is the...

Question