Question 1
A 0.50 kg football is thrown with a velocity of 15 m/s to the right. A stationary receiver catches the ball and brings it to rest in 0.020s . What is the force exerted on the receiver?
So I used mvf-mvi/change(t)
I got 375 for that one...
Question 2
A 0.40 kg soccer ball approaches a player horizontally with a velocity of 18 m/s to the north. The player strikes the ball and causes it to move in the opposite direction with a velocity of 22 m/s. What impulse was delivered to the ball by the player?
I am not sure on this one but I used the formula of: mass * change in velocity and got 1.6 N
Now the last I do not understand and if someone could help me I would really appreciate it:
Question 3
An 82 kg man drops from rest on a diving board 3.0 m above the surface of the water and comes to rest 0.55 after reaching the water. What force does the water exert on him?
I think I may be overthinking this (if that's a word hah) but does gravity play a part here with the 9.8 m/s 2 ?
Please help this assignment is very important to me.
warren moon throws a footbal with a velocity of 20 m/s at an angle of 30 degrees with the horizontal. air resistance may be ignored. how much time is required for the football to reach the highest point of the trajectory
Chejen
Question 1:
To calculate the force exerted on the receiver, you can use Newton's second law of motion, which states that force is equal to mass times acceleration. In this case, we need to find the acceleration first.
Given:
Mass of the football (m) = 0.50 kg
Velocity of the football (v) = 15 m/s
Time taken to bring the ball to rest (Δt) = 0.020 s
First, calculate the acceleration using the formula:
Acceleration (a) = Change in velocity / Time taken
Acceleration (a) = (0 m/s - 15 m/s) / 0.020 s
Acceleration (a) = -750 m/s^2 (negative sign indicates deceleration)
Now, use Newton's second law of motion:
Force (F) = Mass (m) × Acceleration (a)
Force (F) = 0.50 kg × -750 m/s^2
The force exerted on the receiver is -375 N (negative sign indicates that the force is in the opposite direction to the motion).
Question 2:
To find the impulse delivered to the soccer ball, you can use the equation for impulse:
Impulse (J) = Force (F) × Time taken (Δt)
Given:
Mass of the soccer ball (m) = 0.40 kg
Initial velocity of the soccer ball (vi) = 18 m/s (north direction)
Final velocity of the soccer ball (vf) = -22 m/s (opposite direction to the initial velocity)
First, calculate the change in velocity:
Change in velocity (Δv) = Final velocity (vf) - Initial velocity (vi)
Change in velocity (Δv) = -22 m/s - 18 m/s
Change in velocity (Δv) = -40 m/s
Now, use the formula for impulse:
Impulse (J) = Mass (m) × Change in velocity (Δv)
Impulse (J) = 0.40 kg × -40 m/s
The impulse delivered to the ball by the player is -16 N·s (negative sign indicates the change in direction of the ball).
Question 3:
To find the force exerted by the water on the man, you can use the equation for force:
Force (F) = Mass (m) × Acceleration (a)
Given:
Mass of the man (m) = 82 kg
Initial velocity of the man (vi) = 0 m/s (rest)
Final velocity of the man (vf) = 0 m/s (rest)
Distance traveled by the man (d) = 3.0 m
Time taken to reach the water (Δt) = 0.55 s
Gravity (g) = 9.8 m/s^2
First, calculate the acceleration using the formula for distance traveled with constant acceleration:
Distance (d) = Initial velocity (vi) × Time taken (Δt) + 0.5 × Acceleration (a) × (Time taken (Δt))^2
Rearranging the equation, we get:
Acceleration (a) = 2 × (Distance (d) - Initial velocity (vi) × Time taken (Δt)) / (Time taken (Δt))^2
Acceleration (a) = 2 × (3.0 m - 0 m/s × 0.55 s) / (0.55 s)^2
Simplifying the equation:
Acceleration (a) = 2 × (3.0 m / 0.3025 s^2)
Acceleration (a) ≈ 39.67 m/s^2
Now, use the formula for force:
Force (F) = Mass (m) × Acceleration (a)
Force (F) = 82 kg × 39.67 m/s^2
The force exerted by the water on the man is approximately 3,250 N.
Gravity does play a part in this question, as it provides the weight of the man, but it doesn't directly affect the force exerted by the water.
Question 1:
To calculate the force exerted on the receiver, you can use Newton's second law of motion, which states that force (F) is equal to the change in momentum (Δp) divided by the change in time (Δt). In this case, the receiver catches the ball and brings it to rest, so the final momentum (pf) is 0 since the ball is at rest, and the initial momentum (pi) can be calculated using the mass (m) and velocity (vi) of the ball before it was caught.
You correctly used the formula F = Δp/Δt. The change in momentum (Δp) is given by mvf - mvi, where "m" is the mass of the ball. Since the football was caught and brought to rest, the final velocity (vf) is 0 m/s. Using the given mass (m = 0.50 kg) and initial velocity (vi = 15 m/s), you can calculate the change in momentum.
Using the formula, (0.50 kg) * (0 m/s - 15 m/s) / (0.020 s), you will get the force exerted on the receiver in Newtons.
Question 2:
To calculate the impulse delivered to the soccer ball by the player, you can use the formula impulse (J) = change in momentum (Δp) = mass (m) * change in velocity (Δv). Here, the mass of the soccer ball is given as 0.40 kg.
The change in velocity is the final velocity (vf) minus the initial velocity (vi). In this case, the soccer ball is moving in the opposite direction after being struck by the player, so the final velocity is -22 m/s, and the initial velocity is +18 m/s.
Using the formula, (0.40 kg) * ((-22 m/s) - (18 m/s)), you can calculate the impulse delivered to the ball by the player.
Question 3:
In this question, you need to consider both the force of gravity and the force exerted by the water to determine the total force experienced by the man.
First, calculate the gravitational potential energy (PE) of the man at the top of the diving board using the formula PE = mgh, where "m" is mass, "g" is acceleration due to gravity (approximately 9.8 m/s^2), and "h" is the height.
Next, calculate the work done by gravity as the man falls. The work done (W) by gravity is equal to the force applied (F) multiplied by the distance moved (d), which is the height of the board.
Since the man comes to rest in the water, you can calculate the force exerted by the water using the formula F = Δp / Δt, similar to question 1, where Δp is the change in momentum and Δt is the time taken for the man to stop.
To find the change in momentum (Δp), you can multiply the mass of the man (82 kg) by the velocity before entering the water. Since the man drops from rest, the initial velocity (vi) is 0 m/s.
Finally, with the force of gravity acting downward and the force exerted by the water acting upward, the total force experienced by the man can be calculated by subtracting the force due to gravity from the force exerted by the water.