Physics 1 Lab 7 Range Prediction

Total Mechanical Energy (Etot)

The sum of Kinetic Energy (K) and Potential Energy (U).

Formula for Translational Kinetic Energy (Ktrans)

½ mv²

Formula for Gravitational Potential Energy (Ug)

mgh

When is total mechanical energy conserved?

When only conservative forces (like gravity) are present and non-conservative forces (like friction or air resistance) are negligible.

What causes loss of mechanical energy in the presence of friction?

Friction converts mechanical energy into thermal (heat) energy.

Key variable needed to determine the horizontal range (R) of a projectile in this experiment

The exit speed (vexit) of the ball as it leaves the track.

Simplified equation for vexit assuming Conservation of Energy and no friction, starting from height h1 and exiting at height h2

sqroot (2g(h1-h2))

What two variables determine the uncertainty (ΔR) in the predicted range (R)?

The uncertainty in the initial height (Δh) and the uncertainty in the time of flight (Δt).

Equation used to find the time of flight (t) of the ball (assuming viy =0)

y= viyt + ½ gt² => t= sqroot(2y/g)

Final equation for the predicted range (R) in terms of exit speed (vexit) and time (t)

vexitt

R=

v0²sinθ/g

Total Kinetic Energy (Ktotal) for a rolling solid sphere of mass m and speed v

Ktrans + Krot = ½ mv² + 1/5 mv² = 7/10 mv²

Simplified formula for vexit of a rolling sphere (ignoring friction) starting at hi and exiting at hf

sqroot(10/7g(hi-hf)

How is the work done by friction (Wfriction) incorporated into the Conservation of Energy equation?

Ki+Ui+Wfriction = Kf + Uf

Formula for vexit of a rolling sphere considering friction (as potential energy change hbi-hbf )

sqroot (10/7 g (hi-hf-(hbi-hbf)

Formula for the time of flight (T) for a projectile launched from height hf at angle θ

(vesinθ+ sqroot(ve²sin²θ+2ghf))/g

The effect on vexit if friction is ignored in the calculations

The exit velocity would be slightly larger because less energy would be assumed to be lost.