A ball that is attached to a string travels in a horizontal, circular path, as shown in Figure 1. At time t0 , the ball has a speed v0 . The forces exerted on the ball at t0 are represented by the free-body diagram, as shown in Figure 2. At a later time t1 , the tangential speed of the ball is increased to 2v0 . What is the magnitude of the force that the ball exerts on the string at time t1 ?

F₁ = 4 F₀

Explanation:

The force applied on the string by the ball attached to it, while in circular motion will be equal to the centripetal force. Therefore, at time t₀, the force on ball F₀ is given as:

F₀ = mv₀²/r   equation (1)

where,

F₀ = Force on string at t₀

m = mass of ball

v₀ = speed of ball at t₀

r = radius of circular path

Now, at time t₁:

v₁ = 2v₀

F₁ = mv₁²/r

F₁ = m(2v₀)²/r

F₁ = 4 mv₀²/r

using equation (1):

F₁ = 4 F₀

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

we need to know the time interval during which the force acts. impulse of force = momentum change