I need physics help. I don't understand how to do these questions. Can someone show me what I should use? and explain. I'll do calculations by myself.
A stationary curling stone is struck in a glancing collision by a second curling stone of equal
mass. If the first stone moves away at a velocity of 0.92 m/s [N71oW] and the second stone
moves away at a velocity of 1.25 m/s [N44oE], what was the initial velocity of the second stone?
(5 marks)
2. A billiard ball (0.62 kg) with a velocity of 2.0 m/s [N] hits another ball and has a velocity of 1.7
m/s [E] after the collision. Determine the impulse on the ball and the average force exerted on it
during the collision if the duration of the collision was 0.0072 s. (5 marks)
3. Two billiard balls of equal mass undergo a head on collision. The red ball is travelling at 2.1
m/s [right] and hits the blue ball travelling at 3.0 m/s [left]. If the speed of the red ball after the
collision is 3.0 m/s [left], determine the velocity of the blue ball after the collision. (5 marks)
4. A car with a mass of 1800 kg is initially travelling with a velocity of 22 m/s [N] when it collides
with a truck with a mass of 3200 kg traveling with a velocity of 14 m/s [E]. If the two vehicles
become attached during the collision, determine their final velocity. (5 marks)
1. M1 = M2 = M.
Unless otherwise stated, all angles are measured CCW from +x-axis.
M*V1 + M*V2 = M*V3 + M*V4.
M*0 + M*V2 = M*0.92m/s[161o] + M*1.25m/s[46o].
M*V2 = 0.92M[161o] + 1.25M[46o].
Divide both sides by M and solve for V2
V2 = -0.87+0.30i + 0.87+0.90i =
1.20i = 1.20m/s[90o].
3. M*V1 + M*V2 = M*V3 + M*V4.
M*2.1 - M*3 = -M*3 + M*V4.
V4 = ?
4. M1*V1 + M2*V2 = M1*V + M2*V.
1800*22i + 3200*14 = 1800V + 3200V.
Divide both sides by 100 and solve for v.
To solve these problems, you can use the principles of momentum and the law of conservation of momentum. The law of conservation of momentum states that the total momentum of a system remains constant unless acted upon by external forces.
Let's go through each problem step by step:
1. For the first question, we can use the law of conservation of momentum to find the initial velocity of the second stone. Since the first stone was stationary, its initial velocity is 0. We can write the equation as:
(m1 * v1) + (m2 * v2) = (m1 * vf1) + (m2 * vf2)
where m1 and m2 are the masses of the stones, v1 and v2 are the initial velocities of the stones, and vf1 and vf2 are the final velocities of the stones.
Since the stones have equal mass, the equation becomes:
v2 = (m1 * vf1 + m2 * vf2) / m2
Substituting the given values, we have:
v2 = (0 * 0.92 + m2 * 1.25) / m2
Simplifying the equation, we get:
v2 = 1.25 m/s [N44oE]
2. For the second question, we can calculate the impulse on the ball and the average force exerted on it during the collision. The impulse (J) is given by the equation:
J = Δp = m * Δv
where m is the mass of the ball and Δv is the change in its velocity.
The average force (F) can be calculated using the equation:
F = J / Δt
where Δt is the duration of the collision.
Substituting the given values, we have:
J = 0.62 kg * (1.7 m/s - 2.0 m/s) = -0.124 kg·m/s
F = -0.124 kg·m/s / 0.0072 s
Simplifying the equation, we get:
F = -17.22 N
The negative sign indicates that the force is in the opposite direction of motion.
3. For the third question, we can again use the law of conservation of momentum. The equation can be written as:
(m1 * v1) + (m2 * v2) = (m1 * vf1) + (m2 * vf2)
Substituting the given values, we have:
(0.62 kg * 2.1 m/s) + (0.62 kg * 3.0 m/s) = (0.62 kg * 3.0 m/s) + (0.62 kg * vf2)
Simplifying the equation, we get:
vf2 = 2.1 m/s [right]
4. For the fourth question, we can again use the law of conservation of momentum. Since the two vehicles become attached, their final velocity will be the same.
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Substituting the given values, we have:
(1800 kg * 22 m/s) + (3200 kg * 14 m/s) = (1800 kg + 3200 kg) * vf
Simplifying the equation, we get:
vf = (1800 kg * 22 m/s + 3200 kg * 14 m/s) / (1800 kg + 3200 kg)
Simplifying further, we get:
vf = 18.1 m/s [N]
To solve these physics questions, you can use the principles of conservation of momentum and impulse-momentum theorem. I will explain each question and provide a step-by-step guide on how to solve them.
1. Glancing collision of curling stones:
In this question, you need to find the initial velocity of the second stone. To solve it, you can use the principle of conservation of momentum.
Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Momentum is calculated by multiplying mass and velocity.
Step-by-step solution:
1. Calculate the momentum of the first stone:
Momentum = mass * velocity
Momentum = m1 * v1
2. Calculate the momentum of the second stone:
Momentum = mass * velocity
Momentum = m2 * v2
3. Apply the conservation of momentum equation:
m1 * v1 = m2 * v2
4. Rearrange the equation to solve for v2:
v2 = (m1 * v1) / m2
2. Impulse and average force during a billiard ball collision:
This question requires you to find the impulse and average force during a collision between two billiard balls.
Impulse is defined as the change in momentum and can be calculated using the impulse-momentum theorem. The average force exerted on an object is the impulse divided by the time interval over which it acts.
Step-by-step solution:
1. Calculate the initial momentum of the ball:
Momentum = mass * velocity
Momentum = m1 * v1
2. Calculate the final momentum of the ball:
Momentum = mass * velocity
Momentum = m2 * v2
3. Calculate the impulse:
Impulse = Final momentum - Initial momentum
Impulse = m2 * v2 - m1 * v1
4. Calculate the average force:
Average force = Impulse / time
3. Head-on collision of billiard balls:
In this question, you need to find the velocity of the blue ball after the collision.
Step-by-step solution:
1. Apply the principle of conservation of momentum:
m1 * v1(initial) + m2 * v2(initial) = m1 * v1(final) + m2 * v2(final)
2. Substitute the given values into the equation:
m1 * 2.1 + m2 * (-3.0) = m1 * (-3.0) + m2 * v2(final)
3. Rearrange the equation to solve for v2(final):
v2(final) = (m1 * v1(initial) + m2 * (-3.0) - m1 * (-3.0)) / m2
4. Calculate the velocity of the blue ball after the collision.
4. Collision of a car and truck:
In this question, you need to determine the final velocity of the car and truck after they collide.
Step-by-step solution:
1. Calculate the initial momentum of the car:
Momentum = mass * velocity
Momentum_c = m_c * v_c
2. Calculate the initial momentum of the truck:
Momentum = mass * velocity
Momentum_t = m_t * v_t
3. Apply the conservation of momentum equation:
Momentum_c + Momentum_t = (m_c + m_t) * v(final)
4. Rearrange the equation to solve for v(final):
v(final) = (Momentum_c + Momentum_t) / (m_c + m_t)
5. Calculate the final velocity of the car and truck.
Remember to substitute the given values and perform the necessary calculations to solve each question.