Determine the tension in a 40 cm long pendulum when a bob of mass 200g moving at 0.7 m.s is 15 degrees from the vertical?

correction the velocity is 0.7 m/s

The tension in the string minus the weight component in the string direction equals the centripetal force.

T - M*g cos15 = M V^2/R

M = 0.200 Kg
R = 0.40 m
g = 9.8 m/s^2
V = 0.7 m/s

Solve for T.

would the radius be half of the 0.40m?

no radius is .4m.

Thank you!

Two blocks move along a linear path on a nearly frictionless air track. One block, of mass 0.120 kg, initially moves to the right at a speed of 4.90 m/s, while the second block, of mass 0.240 kg, is initially to the left of the first block and moving to the right at 7.40 m/s. Find the final velocities of the blocks, assuming the collision is elastic.

So what is the velocity of the 0.120 kg block and the0.240 kg block?

To determine the tension in a pendulum, we need to consider the forces acting on the bob. The two main forces involved are the gravitational force and the tension force.

First, we calculate the gravitational force acting on the bob. The force of gravity is given by the equation:

Fg = m * g

Where:
Fg is the gravitational force
m is the mass of the bob
g is the acceleration due to gravity (approximately 9.8 m/s^2)

In this case, the mass of the bob is 200 grams, which is equivalent to 0.2 kg. Plugging in these values into the equation, we have:

Fg = 0.2 kg * 9.8 m/s^2

Fg = 1.96 N

Next, we calculate the component of the gravitational force acting in the direction of tension. This component is given by:

Fg_parallel = Fg * sin(theta)

Where:
Fg_parallel is the component of the gravitational force parallel to the pendulum's length
theta is the angle between the pendulum's length and the vertical line

In this case, theta is 15 degrees. Plugging in the values, we have:

Fg_parallel = 1.96 N * sin(15 degrees)

Fg_parallel ≈ 0.508 N

Finally, the tension in the pendulum can be calculated by subtracting the component of the gravitational force parallel to the pendulum's length from the total gravitational force:

Tension = Fg - Fg_parallel

Tension = 1.96 N - 0.508 N

Tension ≈ 1.452 N

Therefore, the tension in the 40 cm long pendulum is approximately 1.452 N.