How far would the block have slid if its initial velocity were increased by a factor of 3.3?

Question

A block of mass 4 kg, sliding on a horizontal plane, is released with a velocity of 2 m/s. The block slides and stops at a distance of 2 m beyond the point where it was released. How far would the block have slid if its initial velocity were increased by a factor of 3.3?

Answer 1

How far would the block have slid if its initial velocity were increased by a factor of 3.3?

A block of mass 4 kg, sliding on a horizontal plane, is released with a velocity of 2 m/s. The block slides and stops at a distance of 2 m beyond the point where it was released. How far would the block have slid if its initial velocity were increased by a factor of 3.3?

The kinetic energy is initially KE(0)=(1/2)mv²(0)=0.5(4 kg)(2 m/sec)² = 8 J

The work done by friction f_k over the 2 m glide is W=f_k(2 m).

The friction is then found by setting W=KE

2f_k=8

f_k=4 N

If the velocity were increased by 3.3X, then KE=(1/2)(4)[(3.3)(2)]²=21.78 J

We know the friction force is constant (it doesn't care about speed) so

again, setting W=KE we get (4D)=21.78

D=5.44 m

Solution: 5 m