a 0.20 kg ball is released from a height of 10 m above the beach; the impression the ball makes in the sand is 5.0 cm deep while the ball stops uniformly. what is the force acting on the ball by the sand?
Initial PE= final force*distance
.2*9.8*10=finalforce*.05
solve for force.
392 N
To determine the force acting on the ball by the sand, we can use the principle of work and energy.
Step 1: Calculate the potential energy of the ball before it hits the sand.
The potential energy (PE) of an object at a certain height h is equal to the product of its mass (m), the acceleration due to gravity (g), and the height (h): PE = mgh
where g is approximately 9.8 m/s^2.
PE = (0.20 kg) * (9.8 m/s^2) * (10 m)
PE = 19.6 J
Step 2: Calculate the work done by the sand to stop the ball.
The work done (W) is equal to the change in potential energy, which can be calculated using the formula: W = PE_final - PE_initial.
Since the ball stops uniformly, the final potential energy (PE_final) is zero, and the work done by the sand is equal to the initial potential energy (PE_initial):
W = 0 J - 19.6 J
W = -19.6 J
Step 3: Calculate the force acting on the ball by the sand.
The work done is equal to the force (F) applied multiplied by the distance (d) over which the force is applied.
Since the work done is negative (as the force opposes the motion), we have:
W = -F * d
Plugging in the values:
-19.6 J = -F * (5.0 cm)
(Note that we need to convert cm to meters: 5.0 cm = 0.05 m)
Simplifying the equation:
-19.6 J = -F * (0.05 m)
Step 4: Solve for the force acting on the ball by dividing both sides of the equation by -0.05 m:
F = -19.6 J / (-0.05 m)
F ≈ 392 N
Therefore, the force acting on the ball by the sand is approximately 392 Newtons.
To determine the force acting on the ball by the sand, we can use the concept of work and energy.
First, let's calculate the gravitational potential energy initially possessed by the ball at a height of 10 m above the beach. The equation for gravitational potential energy is given by:
Potential Energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)
Where:
m = 0.20 kg (mass of the ball)
g = 9.8 m/s² (acceleration due to gravity)
h = 10 m (height above the beach)
PE = 0.20 kg × 9.8 m/s² × 10 m
PE = 19.6 J
Next, we need to calculate the work done by the sand to stop the ball. The work done is equal to the change in potential energy, which is given by:
Work (W) = Potential Energy (PE) final - Potential Energy (PE) initial
Since the ball has stopped, its final potential energy is zero because it is at ground level. Therefore:
W = 0 - 19.6 J
W = -19.6 J
Note that the work done by the sand is negative because the force opposes the motion of the ball.
Now, we can calculate the force acting on the ball by dividing the work done by the displacement. The displacement here is the depth of the impression in the sand, which is 5.0 cm (or 0.05 m).
Force (F) = Work (W) / Displacement (d)
F = -19.6 J / 0.05 m
F = -392 N
Therefore, the force acting on the ball by the sand is -392 N. The negative sign indicates that the force is acting in the opposite direction of the ball's motion, as expected for deceleration.