Your Name: _______________________ PHY203

Exam #2

Student ID: ________________________ Chapters 4-7

Thurs., 10/24/02

Lecture Time: 9 a.m 1p.m. 2p.m. 3p.m. Honors

Score:

1 _________________ (out of 17)

2 _________________ (out of 17)

3 _________________ (out of 33)

4 _________________ (out of 33)

Total _______________

1. A particle of m=2 kg undergoes a displacement of d = -3mi + 6 mj. During the displacement, a constant force, F = 5Ni + 10Nj, acts on the particle. .

a. Calculate the work done by the force in J.

b. Calculate the final velocity of the particle in m/s assuming it started with an initial velocity of 10 m/s before the force was applied.

2. A sphere of mass, m= 2 kg, attached to a string is turning in a vertical circle with radius, r = 0.5 m. At the top of the circle, the particle has a kinetic energy of K = 50J.

a. Sketch the forces on the particle on the diagram above.

b. Calculate the tension, T, in the string in N at the top of the circle..

3. Two blocks, (m₁ =20 kg and m₂ =10kg) are pushed with a horizontal external applied force, F, of magnitude 100N as shown below. Let F_c be the contact force between the two blocks. Assume a frictionless surface.

a. Redraw the blocks and sketch all of the forces on each block (free body diagrams).

b. Write Newton’s 2^nd law (force equation) in both axes for both masses.

c. Calculate the magnitude of the normal force on each block.

d. Calculate the magnitude of the contact force, F_c and the (same) acceleration, a, of the two blocks.

4. A block of mass 5.0 kg. is released on the ramp below at point A and slides 2 meters down a rough 30^o ramp which has a kinetic friction coefficient of m_k = 0.25. The block travels over a frictionless surface between points B and C and then encounters a spring with spring constant, k=8000 N/m.

a. Calculate the energy converted by friction to heat by the block sliding down the ramp.

b. Calculate the kinetic energy point B once it has reached the bottom of the ramp.

c. Calculate the distance by which the spring is compressed to bring the block to rest.

PHY203

Exam #2, F/02

Crib Sheet

Chapters 4-7

(Note: Use 9.81 m/s2 for g, the acceleration due to gravity.)

For constant acceleration(in one dimension):

x_f = x_o + v_ot + (1/2)at2

v_f = v_o + at

v_f2 = v_o2 + 2a(x_f - x_o)

(Note: Bold letters indicate vectors below.)

F = ma

spring force: F = -kDx , where k is the spring constant

weight: W = mg

friction force:

kinetic fk = mkFn , where Fn is the normal force and mk is the kinetic frictional coefficient

static fs < msFn, fsmax = msFn

uniform circular motion

centripetal acceleration: a = v2/R

Work and Energy

W = F ^. d = Fdcosq

Work done by friction = -f_kDs

E_Thermal = |Work done by friction|

Kinetic Energy: K = (1/2)mv²

Potential Energy: U_spring = (1/2)kx²

U_grav = mgh

Total energy, E, is conserved ( a constant).