Answer:
Explanation:
a) First, let's calculate the value of the Friction force, which is given by the formula:
Ff = u*W
As the Friction force has an X component, it would be:
Ff = u*m*g*cosФ
Where m*g is the weight of the child.
Solving for Ff:
Ff = 0.051 * 235cos37 = 9.57 N
Now, to get the energy transferred to thermal energy (or heat) we need to get the Work done, so:
Wf = Ff * d
Wf = 9.57 * 4.9 = 46.9 J
b) We need to get the downslope component of the child weight, which is:
Wy = 235sin37 = 141.43 N
As you can imagine, the gravity also does work, so:
Wg = Wy * d
Wg = 141.43 * 4.9 = 693 J
Now, let's get the kinetic energy, which can be obtained by this expression:
ΔKe = Wg - Wf
ΔKe = 693 - 46.9 = 646.1 J
The formula for kinetic energy is:
Ke = 1/2 m*V^2
We have the innitial speed which is 0.355 m/s, and the mass can be obtained by m*g so:
Fw= m*g ----> m = Fw/g
m = 235 / 9.8 = 23.97 kg
so the innitial energy is:
Ke = 1/2 * 23.97 * (0.355)^2
Ke = 1.51 J
This could be Ke1, so to get Ke2:
ΔKe = Ke2 - Ke1
Ke2 = Δke + Ke1
Ke2 = 646.1 + 1.51 = 647,61 J
Finally, the speed at the bottom would be:
v = √2Ke/m
v = √2*647.61/23.97
v = 7.35 m/s
