1. If m1= 3kg and m2= 2kg then find acceleration and tension action on the system.
2. A batsman deflects a ball by an angle 45 degree without changing its initial speed which is equal to 54km/hr.What is the impulse imparted to the bal.(mass of the ball is .15kg)
1. What system? Is there a figure that goes with this question?
2. Convert the 54 km/h speed to 15.0 m/s. Compute the velocity change vector.
Multiply that by 0.15 kg for the momentum change, which equals the impulse.
54 km/h is a VERY slow pitch (33.5 mph). A 45 degree deflection would be a foul tip.
yes there is a figure with this question but how to draw?
To find the acceleration and tension in question 1, we can use Newton's second law and the concept of tension in a system. Here are the steps to solve the problem:
1. Identify the forces acting on the system: In this case, we have two masses connected by a string. The forces acting on the masses are gravitational force (mg) pulling them downwards and tension (T) pulling them upwards.
2. Write down the equations of motion for each mass:
For m1: sum of forces = m1 * acceleration
For m2: sum of forces = m2 * acceleration
3. Calculate the tensions in the string:
Tension in the string connecting m1 and m2 is the same. Let's call it T.
Tension in the string connecting m1 and the pulley = T1
Tension in the string connecting m2 and the pulley = T2
4. Analyze the forces acting on each mass:
For m1: T1 - m1 * g = m1 * a (Equation 1)
For m2: T2 - m2 * g = -m2 * a (Equation 2)
(Note: Negative sign for m2 acceleration represents that m2 is moving in the opposite direction of m1)
5. Since T = T1 = T2, we can subtract equation 2 from equation 1 to eliminate T1 and T2:
T1 - T2 = (m1 - m2) * a
Substituting the values of m1 and m2, we get:
T = (3 kg - 2 kg) * a
T = 1 kg * a (Equation 3)
6. To find the value of tension (T), we need the acceleration (a). We can solve equations 1 and 2 simultaneously to get the value of 'a'.
7. Solving equations 1 and 2 simultaneously:
T1 = m1 * a + m1 * g
T2 = m2 * g - m2 * a
Substituting the values of m1, m2, and g:
T1 = 3 kg * a + 3 kg * 9.8 m/s^2
T2 = 2 kg * 9.8 m/s^2 - 2 kg * a
Since T1 = T2 = T,
3 kg * a + 3 kg * 9.8 m/s^2 = 2 kg * 9.8 m/s^2 - 2 kg * a
Simplifying the equation:
5 kg * a = 2 kg * 9.8 m/s^2 - 3 kg * 9.8 m/s^2
Calculating the equation:
5 kg * a = 19.6 N
Dividing both sides by 5 kg:
a = 3.92 m/s^2
8. Now, we can substitute the value of 'a' back into Equation 3 to find the tension (T):
T = 1 kg * 3.92 m/s^2
T = 3.92 N
Therefore, the acceleration of the system is 3.92 m/s^2, and the tension in the system is 3.92 N.
For question 2, we can calculate the impulse imparted to the ball using the following steps:
1. Impulse is defined as the change in momentum of an object. The formula for impulse is given as:
Impulse = force * time = mass * change in velocity
2. To find the impulse, we need to find the change in velocity of the ball. Since the initial speed is given in km/hr, we need to convert it to m/s.
Initial speed of the ball = 54 km/hr
Converting to m/s:
Initial speed = 54 km/hr * (1000 m/1 km) * (1 hr/3600 s)
Initial speed = 15 m/s
3. The angle of deflection doesn't change the magnitude of speed, only its direction. So, the final speed of the ball remains 15 m/s.
4. Using the principle of conservation of momentum, the change in velocity can be calculated:
Change in velocity = Initial velocity - Final velocity
Change in velocity = 0 - 15 m/s
Change in velocity = -15 m/s
5. Since the mass of the ball is given as 0.15 kg, we can now calculate the impulse using the formula:
Impulse = mass * change in velocity
Impulse = 0.15 kg * (-15 m/s)
Impulse = -2.25 Ns
Therefore, the impulse imparted to the ball is -2.25 Ns. Note that the negative sign indicates the change in direction of the impulse.