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MATH + SCIENCE Science
INITIATIVE
Example: the box accelerates to the right. Friction is parallel to a, and
weight and normal are perpendicular to a, but tension needs to be broken
into two components: FTsinθ up and FTcosθ to the right.
• Weight is down, normal and FTsinθ are up, and since these forces are
perpendicular to a, they balance each other out: FN + FTsinθ = mg
• FTcosθ is in the same direction as a, so it is a “positive” force.
Friction opposes a, so it is a “negative” force. Because these forces
are parallel to a, they add to ma: FTcosθ – Ff = ma
Multiple-Choice Questions
M1. Apollo 13 is a 1995 movie about a mission to the M3. A skydiver falling through the air opens her
Moon that experiences serious problems. In the parachute. The skydiver and parachute together
movie, an astronaut says, “We just put Sir Isaac have a weight W. At a specific instant after the
Newton in the driver’s seat.” This line, a parachute opens, the force of air resistance on the
reference to Newton’s First Law, is spoken just parachute is 1.4W. What is the acceleration of
after the parachute-and-skydiver system at this
instant?
(A) the rocket begins firing its engines and lifts off
from the launch pad. (A) 14 m/s2 downward
(B) the spacecraft begins firing its engines on its way (B) 4 m/s2 downward
back to Earth from the Moon. (C) 4 m/s2 upward
(C) the spacecraft enters Earth’s atmosphere and air (D) 14 m/s2 upward
resistance begins to slow its descent.
(D) the spacecraft has finished firing its engines and
has spent all of its fuel.
M4. A student hypothesizes that a certain elastic cord
exerts a constant force even as the cord contracts
to its natural length. To test this hypothesis, the
student attaches the cord to a cart and stretches
the cord a significant distance. The student
M2. An aircraft flying to the right has a constant releases the cart and measures the increase in
horizontal speed of 200 m/s has four forces speed Δv of the cart during an interval of time Δt.
acting on it shown above left. When the aircraft If the student performs multiple trials in which
passes through the cloud at point S (shown above the mass M of the cart is varied, which of the
right), the force of thrust has the same magnitude following graphs would yield a line if the cord’s
as the force of drag, and the force of lift balances force were constant?
the force of weight. If this condition continues,
which path shown above right will the plane (A) M vs. (Δv/Δt)
follow? (B) M vs. (Δt/Δv)
(C) M2 vs. (Δv/Δt)
(D) M2 vs. (Δt/Δv)
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