A ball acquires a horizontal speed of 12m/sec when a force is applied for a distance of .50m. If the ball has a mass of 1.0kg what is the force applied? ANSWER: 144N....I'm not sure what formulas I'd apply.
It takes a force of 109N to life a stone straight up. This force gives the stone an acceleration of 12.0m/s2. Calculate the mass of the stone. ANSWER: 5.00kg....Same issue here.
work done = kinetic energy gained
F * .5 = (1/2)(1)(144)
F = 144 N
force up = 109
weight down = m g = 9.81 m
F = m a
(109-9.81 m)= 12 m
109 = 21.81 m
m = 109/21.81 Kg
To solve both problems, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) times acceleration (a). The formula for calculating force is:
F = m * a
For the first problem, we are given the horizontal speed of the ball (v = 12 m/s), the distance the force is applied (d = 0.50 m), and the mass of the ball (m = 1.0 kg).
Step 1: Calculate the acceleration of the ball.
The ball's acceleration (a) can be calculated using the formula for acceleration:
a = (v^2 - u^2)/(2 * d),
where v is the final velocity and u is the initial velocity. Since the ball starts from rest horizontally, the initial velocity is 0 m/s.
a = (v^2 - u^2)/(2 * d)
= (12^2 - 0^2)/(2 * 0.50)
= 144/1
= 144 m/s^2
Step 2: Calculate the force applied.
Using Newton's second law, we can rearrange the formula to solve for force:
F = m * a
= 1.0 kg * 144 m/s^2
= 144 N
Therefore, the force applied is 144 N.
For the second problem, we are given the force required to lift the stone (F = 109 N) and the acceleration of the stone (a = 12.0 m/s^2).
Step 1: Calculate the mass of the stone.
We can rearrange Newton's second law and solve for mass:
F = m * a
m = F/a
= 109 N / 12.0 m/s^2
= 9.08 kg (rounded to two decimal places)
Therefore, the mass of the stone is approximately 9.08 kg.
To solve both of these problems, we can use Newton's second law of motion, which states that the force applied to an object is equal to the product of its mass and acceleration. The equation for this is:
F = m * a
where F is the force applied, m is the mass of the object, and a is the acceleration.
Let's apply this equation to each of the given problems:
Problem 1:
We are given:
- Horizontal speed (velocity) of the ball = 12 m/s
- Distance over which the force is applied = 0.50 m
- Mass of the ball = 1.0 kg
To find the force applied, we need to determine the acceleration of the ball in the horizontal direction. Since the ball is moving horizontally with a constant speed, there is no acceleration in that direction. Therefore, the force applied is zero.
So, there seems to be an error in the answer given for problem 1. If the horizontal speed is constant, there is no force acting on the ball horizontally.
Problem 2:
We are given:
- Force applied to lift the stone vertically = 109 N
- Acceleration of the stone = 12.0 m/s^2
To find the mass of the stone, we rearrange the equation F = m * a to solve for m:
m = F / a
Substituting the given values:
m = 109 N / 12.0 m/s^2
m = 9.083 kg
Therefore, the mass of the stone is approximately 9.083 kg.
In conclusion, for problem 1, if the horizontal speed of the ball is constant, there is no force applied horizontally. For problem 2, using Newton's second law, we calculate the mass of the stone to be approximately 9.083 kg.