How far does the crate slide on the horizontal floor if it continues to experien

Question

How far does the crate slide on the horizontal floor if it continues to experience a friction force of magnitude 4.00 N?

If the crate is given a slight push down the ramp, initially with a speed of 0.90 m/s, what will be the final speed right before it reaches the bottom?

8.7 Crate sliding Down a Ramp A 3.50-kg crate slides down a ramp. The ramp is 1.80 m in length and inclined at an angle of 27.5% as shown in the figure. The crate starts from rest at the top, experiences a constant friction force of magnitude 4.00 N, and continues to move a short distance on the horizontal oor after it leaves the ramp (A) Use energy methods to determine the speed of the crate at the bottom of the ramp KB) How far does the crate slide on the horizontal floor if it continues to experience a friction force of magnitude 4.00 N? A cr ate slides down a ramp under the influence of gravity. The potential energy of the system SOLVE IT decreases, whereas the kinetic energy increases (A) Use energy methods to determine the speed of the crate at the bottom of the ramp Conce magine the crate sliding down the ramp in the figure. Th e larger the friction force, the more slowly the crate slid Categorize We identify the crate, the surface, and the Earth as an isolated system with a nonconservative force acting Analyze Because vi 0, the initial kinetic energy of the system when the crate is at the top of the ramp is zero. If the y coordinate is measured from the bottom of the ramp (the final position of the crate, for which we choose the gravitational potential energy of the system to be zero with the upward direction being positive, then yi 0.831 m Write the conservation of energy equation AK AU AEint for this system Substitute for the energies (0 Solve for vf: (mgyi fkd) (1) Vf Substitute numerical val (3.50 kg)(9.80 m/s (0.831 m) (4.00 N)(1.80 m)] Vf 3.50 kg m/s 3.01 KB) How far does the crate slide on the horizontal floor if it continues to experience a friction force of magnitude 4 N? Analyze This part of the problem is han d in exactly the same way as part (A), but in this case we can consider the mechanical energy of the system to consist only of kinetic energy because the potential energy of the system remains fixed Write the conservation of energy equation AK AEint for this situation Substitute for the energies Solve for the distance d and substitute (3.50 kg)(vf 2(4.00 N) 3.95949 X m Finalize For comparison, you may want to calculate the speed of the crate at the bottom of the ramp in the case in which the ramp is fri ctionless. Also notice that the increa ase in internal energy of the system the crate slides down the ramp is 7.20 J. This energy s shared between the ate and the surface, each of which is a bit warmer than before Also notice that the distance d the obj ect slides on the horizontal surface is infinite if the su rface is frictionless Is that consistent with your conceptualization of the situation? GETTING STARTED I STUCK MASTER IT HINTS If the crate is given a slight push down the ramp, in tially with a speed of 0.90 m/s, wl hat wi be the final speed right before it reaches the bottom? m/s

Explanation / Answer

Part b) The calculations shown in part B of the problem are correct but after subsituting the Vi = 3.01 m/s , I am getting d = 3.9638 m

Part c) If the crate has initial velocity Ui = 0.9 m/s

then as shown in question we can use the similar energy conservation equation with slight modification i.e include the initial KE

Hence we get

(1/2*m*Vf2 - 1/2*m*Ui2 ) + ( 0 - mgYi) + Fkd = 0

(0.5*3.5*Vf - 0.5*3.5*0.92 ) + (- 3.5*9.81*0.831) + 4*1.8 = 0

1.75Vf2 - 1.42 - 28.53 + 7.2 = 0

Vf2 = 13 m/s

Vf = 3.6 m/s

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