Question

In a physics lab experiment, a compressed spring launches a 36 g metal ball at a 35 ∘ angle. Compressing the spring 20 cm causes the ball to hit the floor 2.0 m below the point at which it leaves the spring after traveling 5.9 m horizontally. Part A What is the spring constant? Express your answer to two significant figures and include the appropriate units.

Answer 1

We have to use the concept of projectile. By considering the motion along horizontal and vertical directions which will give us the launch velocity. Therefore, launch velocity provides us the spring constant by energy conservation.

● Givens :

Mass of the ball, m = 36 g = 0.036 kg

Launching angle, = 35°

Spring compression, x = 20 cm = 0.2 m

Vertical distance covered, S = 2 m

Horizontal distance, R = 5.9 m

Let us assume that the spring constant is k and launching velocity be v.

Now, the initial velocity akong the x-direction will be v_x = v cos

Let us assume that it takes time t to reach the ground.

Therefore,

  

Now, the initial velocity in the vertical direction is v_y = v sin

Now consider the vertical motion, we can write,

  

[ -g , since it is falling down.]

Now, putting the values,

Now, from the conservation of energy, we can write,

Spring constant, k = 37 N/m