A particle experiences three forces: F₁ = (3i + 4j) N, F₂ = (-2i + 5j) N, and F₃ = (5i - 7j) N. If the particle has mass 2 kg and is initially at rest, which vector equation correctly represents its acceleration?

A block of mass `m` slides down a frictionless inclined plane making an angle `θ` with the horizontal. What is the apparent weight of the block perpendicular to the plane?

Two objects with masses m₁ = 2 kg and m₂ = 4 kg are connected by a massless string over a frictionless pulley. If the system is released from rest, what principle explains why the system cannot remain at rest?

Which condition must be true for a system to have unbalanced forces?

A physics student derives an expression for the work required to lift an object of mass `m` from Earth's surface to a height `h`, where `h << R_{Earth}`. Which expression is correct?

A particle falls from rest in a medium where the resistive force is proportional to velocity (F_r = bv). If the terminal velocity is v_t, what fraction of the terminal velocity is reached after the particle has fallen for a time equal to m/b, where m is the mass of the particle?

An electron with charge -e moves with constant velocity v through a region containing both electric field E and magnetic field B. Which relationship between these fields must be true?

A particle moves in a viscous medium where it experiences a drag force proportional to its velocity (F_drag = -bv). If the particle has an initial velocity v₀ and no other forces act on it, under what condition will its velocity approach zero?

A small object is attached to a string and swung in a horizontal circle on a frictionless table. If the radius of the circle is doubled while maintaining the same centripetal force, how does the speed of the object change?

What happens to kinetic friction if the normal force doubles?

How does static friction respond to applied force?

A particle of mass 2 kg experiences a resistive force $$F = -4v$$ (in newtons). If the particle starts with an initial velocity of 10 m/s, what is the terminal velocity, and how long does it take for the velocity to reduce to $$1/e$$ of its initial value?

A particle of mass `m` moves along the x-axis under the influence of a force `F(x) = -kx`, where `k` is a positive constant. Under what condition will the particle's velocity be zero?

An elevator accelerates upward at 3.0 m/s². If a 70 kg passenger stands on a scale inside, what is the ratio of the passenger's apparent weight to their actual weight?

A block of mass `m` slides down a frictionless inclined plane making an angle `θ` with the horizontal. If a coordinate system is chosen with the x-axis parallel to the incline and the y-axis perpendicular to the incline, what is the net force component along the x-axis?

A 5.0 kg crate rests on a ramp inclined at 20° to the horizontal. The coefficients of static and kinetic friction between the crate and ramp are μₛ = 0.45 and μₖ = 0.30, respectively. What minimum force parallel to the ramp is required to start the crate moving up the ramp?

A 5.0 kg block rests on a frictionless horizontal surface with three horizontal forces acting on it: F₁ = 20 N east, F₂ = 15 N north, and F₃ = 25 N at an angle of 53° south of west. What additional force F₄ is required to maintain translational equilibrium?

A block of mass m slides down a frictionless inclined plane making an angle θ with the horizontal. Which expression correctly describes the condition for the block's velocity to increase?

A person stands on a scale in an elevator. When will the scale reading equal the person's true weight?

A box of mass m is placed on a rough inclined plane with coefficient of static friction μs. The incline makes an angle θ with the horizontal, where sin θ < μs cos θ. Using a coordinate system with one axis parallel to the incline, which equation correctly represents the condition for the box to remain at rest?