A 20 kg sled slides over the crest of an icy drop at 3.5 m/s. The drop is 5 m. Friction on the ice is negligible.
How fast is the sled moving at the bottom?
Well, run the gatekeeper scan first: icy surface, friction negligible, no collision. Mechanical energy is conserved, so the totals at the two snapshots must match.
Take g = 9.8 N/kg, and the bottom as h = 0. Fill the first snapshot's column: KE is (0.5 × 20) × (3.5 × 3.5), which is 122.5 J; GPE is (20 × 9.8) × 5, which is 980 J; the total is 1102.5 J.
At the bottom, GPE is 0 J, so the whole 1102.5 J sits in the kinetic store.
Unpack the bottom's kinetic store: double the 1102.5 J and divide by the 20 kg, so v² = 2205 / 20 = 110.25, and v = 10.5 m/s.
The whole move is a two-column state table and one match: write each snapshot's stores, set the totals equal, and solve for the missing entry.
A 20 kg sled passes the top of a 5 m icy drop at 3.5 m/s, friction negligible. Take g = 9.8 N/kg. Calculate its speed at the bottom.
Write down the values:
m = 20 kg, v_i = 3.5 m/s, h_i = 5 m, h_f = 0 m, g = 9.8 N/kg, v_f = ?
Write down the equation:
KE_i + GPE_i = KE_f + GPE_f
The first column: KE_i = (0.5 × 20) × (3.5 × 3.5), which is 122.5 J; GPE_i = (20 × 9.8) × 5, which is 980 J; a total of 1102.5 J.
Substitute in the values, and calculate:
KE_f = 1102.5 J, then v_f² = 2205 / 20 = 110.25
The sled's speed at the bottom is 10.5 m/s.
A 40 kg skateboarder crosses the lip of a smooth concrete dip at 4.2 m/s. The dip is 1.6 m deep, and friction is negligible. Take g = 9.8 N/kg. Enter her speed at the bottom of the dip in m/s.
A 0.5 kg toy car enters the top of a smooth 1 m ramp at 2.1 m/s, friction negligible. Take g = 9.8 N/kg. Enter its speed at the foot of the ramp in m/s.
The same sled passes a marker 1.4 m below the crest. Calculate its speed at the marker.
Write down the values:
m = 20 kg, v_i = 3.5 m/s, drop so far = 1.4 m, g = 9.8 N/kg, v_f = ?
Write down the equation:
KE_i + GPE_i = KE_f + GPE_f
The GPE given up so far: (20 × 9.8) × 1.4, which is 274.4 J, so KE at the marker is 122.5 + 274.4 = 396.9.
Substitute in the values, and calculate:
v_f² = 793.8 / 20 = 39.69
The sled's speed at the marker is 6.3 m/s.
A loaded 25 kg sled slides at 8.4 m/s across icy ground, friction negligible, toward a smooth rise 2 m high. Take g = 9.8 N/kg. Enter its speed at the top of the rise in m/s.
A 60 kg sledder crosses a crest at 6.3 m/s and rides the icy, friction-negligible slope 1 m down to a flat section. Take g = 9.8 N/kg. Enter the sledder's speed on the flat section in m/s.
A 500 kg roller coaster car crests a hill at 8.4 m/s, then descends 2.8 m on friction-negligible track to a camera point. Take g = 9.8 N/kg. Enter the car's speed at the camera point in m/s.
A water-park slide drops 10 m from the launch deck to the splash pool. A 45 kg rider sets off from rest at the top, and the wet slide keeps friction negligible. Take g = 9.8 N/kg. Enter the rider's speed at the bottom of the slide in m/s.