A 2 kg steel ball strikes a wall with a speed
of 13.9 m/s at an angle of 54.5
◦ with the
normal to the wall. It bounces off with the
same speed and angle, as shown.
If the ball is in contact with the wall for
0.277 s, what is the magnitude of the average
force exerted on the ball by the wall?
Answer in units of N.
the component of velocity normal to the wall is reversed on impact, the other component stays the same.
So the change of momentum is dependent on this part of velocity.
changemomentum=2*mass*cos54.5*13.9
the 2 in front is because the initial normal momentum is reversed.
Impulse=changemomentum
Force*time=2*2*13.9cos54.5
solve for force.
To find the magnitude of the average force exerted on the ball by the wall, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the rate of change of its momentum (p) over time (t). Mathematically, it can be written as:
F = Δp / t
In this case, since the ball bounces off with the same speed and angle, the change in momentum (Δp) will be equal to two times the initial momentum (p).
To determine the initial momentum of the ball, we need to calculate the horizontal and vertical components of the velocity.
The horizontal component of the velocity (Vx) can be found using trigonometry:
Vx = V * cos(θ)
where V is the speed of the ball and θ is the angle with the normal to the wall.
Substituting the given values:
V = 13.9 m/s
θ = 54.5 ◦
Vx = 13.9 m/s * cos(54.5 ◦)
Next, we calculate the vertical component of the velocity (Vy):
Vy = V * sin(θ)
Substituting the given values:
V = 13.9 m/s
θ = 54.5 ◦
Vy = 13.9 m/s * sin(54.5 ◦)
Now, using the given contact time (t = 0.277 s), we can calculate the change in momentum (Δp):
Δp = 2p = 2m * Δv
Where m is the mass of the ball and Δv is the change in velocity, which is equal to 2 * Vy, since the ball bounces off with the same speed and angle.
Substituting the given values:
m = 2 kg
Δv = 2 * Vy
Finally, we can calculate the magnitude of the average force exerted on the ball by the wall by dividing Δp by the contact time (t) and converting it to Newtons:
F = Δp / t
Substituting the calculated values and solving for F will give us the answer in units of Newtons.