An m=150 g block hits an M= 265 g block initially at rest on a horizontal surface. After impact they stick together and slide 7.47 m before coming to rest. The coefficient of friction between blocks and surface is 0.39.
a) What is in m/s the speed of both blocks immediately after impact?
b) What is in m/s the speed of the first block (m) just before impact?
The two blocks decelerate due to friction Ffr=(m1+m2)a a=Ffr/(m1+m2) Ffr=u(m1+m2)g a=u(m1+m2)g/(m1+m2) cancelling the common parameter,a=ug a=0.39*10=3.9m/s Vf=sqrt(2*3.9*7.47)=7.63m/s b)150v1=(150+265)*7.63 v1=21.1m/s
To answer these questions, we can use the principles of conservation of momentum and the work-energy theorem. Here are the steps to find the solutions:
a) To find the speed of both blocks immediately after impact, we need to use the principle of conservation of momentum. The formula for conservation of momentum is:
m1 * v1i + m2 * v2i = (m1 + m2) * vf
Where m1 and m2 are the masses of the blocks, v1i and v2i are their initial velocities, and vf is the final velocity of both blocks after impact.
In this case, the mass of the m block (m1) is 150 g, which is equivalent to 0.15 kg, and the mass of the M block (m2) is 265 g, equivalent to 0.265 kg. The M block is initially at rest, so v2i = 0.
The equation becomes:
0.15 kg * v1i + 0.265 kg * 0 = (0.15 kg + 0.265 kg) * vf
Simplifying further:
0.15 kg * v1i = 0.415 kg * vf
Now, we need to use another piece of information given in the question. The blocks slide together and come to rest after sliding a distance of 7.47 m. From this information, we can apply the work-energy theorem to find vf.
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, the initial kinetic energy of the blocks is zero, as they start from rest. The work done on the blocks is due to the force of friction between the blocks and the surface. The work done can be calculated as:
Work = Force * Distance * cos(θ)
In this case, the force is the force of friction, which can be calculated as:
Force = coefficient of friction * normal force
The normal force on the blocks is equal to the weight of the blocks, which can be calculated as:
Weight = mass * gravity
Here, the coefficient of friction is given as 0.39, and gravity is approximately equal to 9.8 m/s^2.
Let's proceed with these calculations to find vf.
b) To find the speed of the first block (m) just before impact, we need to use the principle of conservation of momentum again. Since the M block is initially at rest, its initial velocity (v2i) is zero. The equation becomes:
m1 * v1i + m2 * v2i = (m1 + m2) * vf
Plugging in the values:
0.15 kg * v1i + 0.265 kg * 0 = (0.15 kg + 0.265 kg) * vf
Simplifying further, solve for v1i.
Following these steps, we can find the answers to both questions.