a 20N sphere A is released from rest when angle at A is 90° and strike a 25 N block B which is at rest.if coefficient of restitution between the sphere and block is 0.75 and that the coefficient of kinetic friction between block and floor is 0.25. How far block B will move
To calculate the distance Block B will move when Sphere A strikes it, we need to consider the conservation of momentum and the effects of friction.
1. Calculate the initial momentum of Sphere A:
Momentum = Mass × Velocity
The mass of Sphere A is not given, but we can calculate it using the weight (force of gravity) acting on it.
Weight = Mass × Gravity
20N = Mass × 9.8 m/s^2 (assuming standard gravity)
Mass = 20N / 9.8 m/s^2
Mass = 2.04 kg (approx.)
Since Sphere A is released from rest, its initial velocity is zero. Therefore, the initial momentum of Sphere A is also zero.
2. Determine the velocity of Block B after the collision:
According to the coefficient of restitution (e), the relative speed of separation after the collision is given by:
Relative speed of separation = e × (Relative speed of approach)
Relative speed of approach = Velocity of A - Velocity of B
Since Sphere A is released from rest, its velocity is zero.
Velocity of A - Velocity of B = 0 - Velocity of B
Relative speed of separation = e × (0 - Velocity of B) (negative sign because the objects move in opposite directions after the collision)
Relative speed of separation = -0.75 × Velocity of B
3. Apply the conservation of momentum:
Before the collision: Momentum of A = 0
After the collision: Momentum of A + Momentum of B = 0
Momentum of B = Mass of B × Velocity of B
Mass of B is not given, but we can find it using the weight (force of gravity) acting on it:
25N = Mass of B × 9.8 m/s^2
Mass of B = 25N / 9.8 m/s^2
Mass of B = 2.55 kg (approx.)
Momentum of B = 2.55 kg × Velocity of B
Now, we can write the conservation of momentum equation:
0 + 2.55 kg × Velocity of B = 0
Solving for Velocity of B:
Velocity of B = 0
Note that the velocity of block B after the collision is zero since Sphere A is not able to transfer any momentum to Block B.
4. Calculate the frictional force acting on Block B:
Frictional force = Coefficient of Kinetic Friction × Normal force
The normal force is equal to the weight of Block B (25N).
Frictional force = 0.25 × 25N
Frictional force = 6.25N
5. Calculate the acceleration of Block B:
Net force acting on Block B = Frictional force
Net force = Mass of B × Acceleration of B
6.25N = 2.55 kg × Acceleration of B
Solving for Acceleration of B:
Acceleration of B = 6.25N / 2.55 kg
Acceleration of B = 2.45 m/s^2 (approx.)
6. Calculate the distance Block B will move:
The equation to calculate the distance traveled by an object with constant acceleration is:
Distance = (Initial velocity × Time) + (0.5 × Acceleration × Time^2)
Since the initial velocity of Block B is zero:
Distance = 0.5 × Acceleration × Time^2
We need to find the time it takes for Block B to come to a stop.
Velocity of B = Acceleration of B × Time
0 = 2.45 m/s^2 × Time
Solving for Time:
Time = 0
The time it takes for Block B to come to a stop is zero.
Therefore, the distance traveled by Block B when Sphere A strikes it is also zero.